Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int k;
  cin >> k;
  long long int p = sqrt(k * 2);
  long long int num, c, q;
  bool flag = 0;
  while (1) {
    num = p * (p + 1) / 2;
    long long int diff = num - k;
    q = diff / p;
    while (num > k) {
      c = p * q - q * q;
      if (c > diff) {
        break;
      } else if (c == diff) {
        flag = 1;
        break;
      } else {
        q++;
        if (q == ceil(p / 2) + 1) {
          break;
        }
      }
    }
    p++;
    if (flag == 0) {
      int max_value = (ceil(p / 2)) * p / 2;
      if (diff > max_value) {
        break;
      }
    } else if (flag == 1)
      break;
  }
  if (flag == 1) {
    cout << "YES\n";
  } else {
    cout << "NO\n";
  }
  return 0;
}